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Unformatted text preview: Conversely, assume that ( x ) is a sequence in ℜ with → for every coordinate . Choose some > 0. For every , there exists some integer such that ∣ − ∣ < for every ≥ Let = max { 1 , 2 ,..., } . Then ∣ − ∣ < for every ≥ and ∥ x − x ∥ ∞ = max ∣ − ∣ < for every ≥ That is, x → x . A similar proof can be given using the Euclidean norm ∥⋅∥ 2 , but it is slightly more complicated. This illustrates an instance where the sup norm is more tractable. 1.215 1. Let ⊆ be closed and bounded and let x be a sequence in . Every term x has a representation x = ∑ =1 x Since is bounded, so is x . That is, there exists such that ∥ x ∥ ≤ for all...
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This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.
 Fall '10
 Dr.DuMond
 Macroeconomics

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